Finding Missing Dimensions in Geometry Practice

Volume of 3D Shapes

• The volume of a cylinder can be found by calculating the area of its base (πr^2) and multiplying it by its height (h).

Spheres

• A sphere with a volume of 4,500π cubic inches has a radius that can be found by rearranging the formula for the volume of a sphere (V = (4/3)πr^3).
• A unit sphere is not a good unit of volume measurement for all spheres because spheres come in different sizes.

Cones

• The volume of a cone can be found by calculating the area of its base (πr^2) and multiplying it by its height (h) divided by 3.
• If a cone has a volume of 240π cubic meters and a height of 5 meters, its radius can be found by rearranging the formula for the volume of a cone.
• If a cone has a volume of 735π cubic millimeters and a height of 5 millimeters, its radius can be found by rearranging the formula for the volume of a cone.

Cylinders

• The radius of a cylinder affects its volume, with a larger radius resulting in a greater volume.
• If a cylinder has a radius of 13 inches and another cylinder has a radius of 10 inches, the taller cylinder will be the one with the larger radius.
• If the diameter of a mug is increased while keeping its height constant, its volume will increase.
• The general relationship between the radius and height in cylinders is that as the radius increases, the volume increases, and as the height increases, the volume also increases.

Practice finding missing dimensions in geometric shapes like cylinders and cones. Calculate the height or radius based on the given volume and one of the dimensions. Examples involve both cylinders and cones of different measurements.